Certified Robustness via Randomized Smoothing over Multiplicative Parameters

Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters. Using this method we construct certifiably robust classifiers with respect to a gamma correction perturbation and compare the result with classifiers obtained via other smoothing distributions (Gaussian, Laplace, uniform). The experiments show that asymmetrical Rayleigh distribution allows to obtain better certificates for some values of perturbation parameters. To the best of our knowledge it is the first work concerning certified robustness against the multiplicative gamma correction transformation and the first to study effects of asymmetrical distributions in randomized smoothing.